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This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com­ invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli­ cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar­ kets, engineering mechanics, optimal control and asset pricing. Further­ more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im­ portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.

A strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students'performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW'Information Technology and Mathematical Problem Solving Research', held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a'chaotic field'in which progress has been quite slow.

The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe­ matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g., does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g., what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus'activity, to whom this volume is dedicated. They range from real analysis to DNA com­ puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical'open problems'. They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

I think the next century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don't know how the laws?t together, and what happens under extreme conditions. But I expect we will?nd a complete uni?ed theory sometime this century. There is no limit to the complexity that we can build using those basic laws. Stephen Hawking, January 2000. We don't know what we are talking about. Many of us believed that string theory was a very dramatic break with our previous notions of quantum theory. But now we learn that string theory, well, is not that much of a break. The state of physics today is like it was when we were mysti?ed by radioactivity. They were missing something absolutely fundamental. We are missing perhaps something as profound as they were back then. Nobel Laureate David Gross, December 2005. This volume is essentially a compilation of papers presented at the Int- national Workshop on Mathematics and Physics of Complex and Nonlinear Systems that was held at Indian Institute of Technology Kanpur, March 14 – 26, 2004 on the theme ChaNoXity: The Nonlinear Dynamics of Nature.

This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods'journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing – making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

This textbook helps future data analysts comprehend aggregation function theory and methods in an accessible way, focusing on a fundamental understanding of the data and summarization tools. Offering a broad overview of recent trends in aggregation research, it complements any study in statistical or machine learning techniques. Readers will learn how to program key functions in R without obtaining an extensive programming background.Sections of the textbook cover background information and context, aggregating data with averaging functions, power means, and weighted averages including the Borda count. It explains how to transform data using normalization or scaling and standardization, as well as log, polynomial, and rank transforms. The section on averaging with interaction introduces OWS functions and the Choquet integral, simple functions that allow the handling of non-independent inputs. The final chapters examine software analysis with an emphasison parameter identification rather than technical aspects.This textbook is designed for students studying computer science or business who are interested in tools for summarizing and interpreting data, without requiring a strong mathematical background. It is also suitable for those working on sophisticated data science techniques who seek a better conception of fundamental data aggregation. Solutions to the practice questions are included in the textbook.

This book presents a collection of results from the interdisciplinary research project “ELLI” published by researchers at RWTH Aachen University, the TU Dortmund and Ruhr-Universität Bochum between 2011 and 2016. All contributions showcase essential research results, concepts and innovative teaching methods to improve engineering education. Further, they focus on a variety of areas, including virtual and remote teaching and learning environments, student mobility, support throughout the student lifecycle, and the cultivation of interdisciplinary skills.

These essays have been written to honor W. W. Bledsoe, a scientist who has contributed to such diverse fields as mathematics, systems analysis, pattern recognition, biology, artificial intelligence, and automated reasoning. The first essay provides a sketch of his life, emphasizing his scientific contributions. The diversity of the fields to which Bledsoe has contributed is reflected in the range of the other essays, which are original scientific contributions by some of his many friends and colleagues. Bledsoe is a founding father of the field of automated reasoning, and a majority of the essays are on that topic. These essays are collected together here not only to acknowledge Bledsoe's manifold and substantial scientific contributions but also to express our appreciation for the great care and energy that he has devoted to nurturing many of the scientists working in those scientific fields he has helped found. Robert S. Boyer Austin February, 1991 ix Acknow ledgements Thanks to Larry Wos, editor of the Journal of Automated Reasoning, and Derek Middleton and Martin Scrivener, Kluwer Academic editors, for sup­ porting the idea of initiating this collection of essays. Thanks to A. Michael Ballantyne and Michael Spivak, for help with lffi.TWC, especially in identifying many formatting problems and providing fixes.

This book presents the application of some AI related optimization techniques in the operation and control of electric power systems. With practical applications and examples the use of functional analysis, simulated annealing, Tabu-search, Genetic algorithms and fuzzy systems for the optimization of power systems is discussed in detail. Preliminary mathematical concepts are presented before moving to more advanced material. Researchers and graduate students will benefit from this book. Engineers working in utility companies, operations and control, and resource management will also find this book useful. ​

Humanity's most basic intellectual quest to decipher nature and master it has led to numerous efforts to build machines that simulate the world or communi­ cate with it [Bus70, Tur36, MP43, Sha48, vN56, Sha41, Rub89, NK91, Nyc92]. The computational power and dynamic behavior of such machines is a central question for mathematicians, computer scientists, and occasionally, physicists. Our interest is in computers called artificial neural networks. In their most general framework, neural networks consist of assemblies of simple processors, or'neurons,'each of which computes a scalar activation function of its input. This activation function is nonlinear, and is typically a monotonic function with bounded range, much like neural responses to input stimuli. The scalar value produced by a neuron affects other neurons, which then calculate a new scalar value of their own. This describes the dynamical behavior of parallel updates. Some of the signals originate from outside the network and act as inputs to the system, while other signals are communicated back to the environment and are thus used to encode the end result of the computation.

Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with artificial intelligence, and in particular agents, multiagent systems and nonmonotonic logic.

“Fuzzy Control - the revolutionary computer technology that is changing our world” - these and other headlines could be read when in the early 90's news from Japan came over telling us about the success of fuzzy controllers. The idea which was put into practice had been suggested by Lot? A. Zadeh in Berkeley in 1965. It had been developed and tested in some practical - plications, especially in Europe. In Japan fuzzy control was celebrated as a technology re?ecting the Japanese way of thinking by its unsharpness and - plicitoverlappingofseveralstatements. Anewtechnologyboomwaspredicted for Japan which would make Europe lose ground. Consequently, this news created unrest. Research projects were initiated and development departments were engaged to translate fuzzy control into products. Adversaries and supporters hurried up to inform themselves and intensely discussed whether the “conventional” or the fuzzy control were the better alternative. Finally, the excitement cooled down since in recent years fuzzy control was analyzed fromthe classical pointofview. Thus,amoreobjective evaluation of its strong and weak points was possible. Furthermore, it was shown how fuzzy systems could be put to use in the steering level which is the level above the control loop, especially in interaction with other methods of soft computing and arti?cial intelligence. Based on these fundamentals, the aim of this book is to support the convenient use of fuzzy controllers and fuzzy systems in the branch of control engineering and automation systems.

Petri nets do not designate a single modeling formalism. In fact, newcomers to the field confess sometimes to be a little puzzled by the diversity of formalisms that are recognized under this'umbrella'. Disregarding some extensions to the theoretical modeling capabilities, and looking at the level of abstraction of the formalisms, Condition/Event, Elementary, Place/Transition, Predicate/Transition, Colored, Object Oriented... net systems are frequently encountered in the literature. On the other side, provided with appropriate interpretative extensions, Controled Net Systems, Marking Diagrams (the Petri net generalization of State Diagrams), or the many-many variants in which time can be explicitly incorporated -Time(d), Deterministic, (Generalized) Stochastic, Fuzzy...- are defined. This represents another way to define practical formalisms that can be obtained by the'cro- product'of the two mentioned dimensions. Thus Petri nets constitute a modeling paradigm, understandable in a broad sense as'the total pattern of perceiving, conceptualising, acting, validating and valuing associated with a particular image of reality that prevails in a science or a branch of science'(Thomas S. Kuhn).